SEM代码篇—-R详细实现（SEM 2）

SEM代码篇----R详细实现

1. step1：安装包

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# install.packages("lavaan")
#install.packages("semPlot")
#install.packages("semTools")

1	rm(list=ls()) #清除所有变量

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library(lavaan)
library(semPlot)
library(semTools)

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This is lavaan 0.6-7

lavaan is BETA software! Please report any bugs.

Warning message:
"package 'semPlot' was built under R version 3.5.3"

###############################################################################

This is semTools 0.5-3

All users of R (or SEM) are invited to submit functions or ideas for functions.

###############################################################################

2. lavvan 语法简介

主要公式类型和其他运算符

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cfa()和sem()拟合函数的参数

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sem(model = NULL, data = NULL, meanstructure = "default",
fixed.x = "default", orthogonal = FALSE, std.lv = FALSE,
parameterization = "default", std.ov = FALSE, missing = "default",
ordered = NULL, sample.cov = NULL, sample.cov.rescale = "default",
sample.mean = NULL, sample.nobs = NULL, ridge = 1e-05, group = NULL,
group.label = NULL, group.equal = "", group.partial = "",
group.w.free = FALSE, cluster = NULL, constraints = "",
estimator = "default",
likelihood = "default", link = "default", information = "default",
se = "default", test = "default", bootstrap = 1000L, mimic = "default",
representation = "default", do.fit = TRUE, control = list(),
WLS.V = NULL, NACOV = NULL,
zero.add = "default", zero.keep.margins = "default",
start = "default", verbose = FALSE, warn = TRUE, debug = FALSE)

lavvan()拟合函数的参数

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lavaan(model = NULL, data = NULL, model.type = "sem",
meanstructure = "default",
int.ov.free = FALSE, int.lv.free = FALSE, fixed.x = "default",
orthogonal = FALSE, std.lv = FALSE, parameterization = "default",
auto.fix.first = FALSE, auto.fix.single = FALSE, auto.var = FALSE,
auto.cov.lv.x = FALSE, auto.cov.y = FALSE, auto.th = FALSE,
auto.delta = FALSE, std.ov = FALSE, missing = "default",
ordered = NULL, sample.cov = NULL, sample.cov.rescale = "default",
sample.mean = NULL, sample.nobs = NULL, ridge = 1e-05, group = NULL,
group.label = NULL, group.equal = "", group.partial = "",
group.w.free = FALSE, cluster = NULL, constraints = "",
estimator = "default",
likelihood = "default", link = "default", information = "default",
se = "default", test = "default", bootstrap = 1000L, mimic = "default",
representation = "default", do.fit = TRUE, control = list(),
WLS.V = NULL, NACOV = NULL,
zero.add = "default", zero.keep.margins = "default",
start = "default", slotOptions = NULL, slotParTable = NULL,
slotSampleStats = NULL, slotData = NULL, slotModel = NULL,
verbose = FALSE, warn = TRUE, debug = FALSE)

提取函数:检查合适的模型

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3. SEM形式

示例数据生成

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set.seed(1)
n=100
x1 <- rnorm(n) * 10
x2 <- rnorm(n) * 10
x3 <- rnorm(n) * 10
x4 <- rnorm(n) * 10
y <- 100 + 5*x1 + (-2)*x2 + 1*x3 + 0.1*x4 + rnorm(n, sd=40)
y1 <- 100 + 5*x1 + (-2)*x2 + 1*x3 + 0.1*x4 + rnorm(n, sd=40)
y2 <- 10 + 0.5*x1 + (-2.5)*x2 + 0.1*x3 + 1*x4 + rnorm(n, sd=20)
x5 <- rbeta(n,2,5)
x6 <- rchisq(n,5)
x7 <- rnorm(n,5)
myData <- data.frame(y,x1,x2,x3,x4,y1,y2,x5,x6,x7)
# write.csv(myData, file = "semData1.csv")#保存匹配数据
# myData <- read.csv("semData1.csv",header = TRUE)

简单回归示例

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回归模型：
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sem_Model1 <- ' y ~ x1+x2+x3+x4 '
#线性回归
fit1_1 <- lm(formula = sem_Model1, data = myData)
summary(fit1_1)

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Call:
lm(formula = sem_Model1, data = myData)

Residuals:
Min 1Q Median 3Q Max
-102.372 -29.458 -3.658 27.275 148.404

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 97.7210 4.7200 20.704 <2e-16 ***
x1 5.7733 0.5238 11.022 <2e-16 ***
x2 -1.3214 0.4917 -2.688 0.0085 **
x3 1.1350 0.4575 2.481 0.0149 *
x4 0.2707 0.4779 0.566 0.5724
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 46.74 on 95 degrees of freedom
Multiple R-squared: 0.5911, Adjusted R-squared: 0.5738
F-statistic: 34.33 on 4 and 95 DF, p-value: < 2.2e-16

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# lavaan
fit1_2 <- sem(model = sem_Model1,data = myData)
summary(fit1_2)

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lavaan 0.6-7 ended normally after 32 iterations

Estimator ML
Optimization method NLMINB
Number of free parameters 5

Number of observations 100

Model Test User Model:

Test statistic 0.000
Degrees of freedom 0

Parameter Estimates:

Standard errors Standard
Information Expected
Information saturated (h1) model Structured

Regressions:
Estimate Std.Err z-value P(>|z|)
y ~
x1 5.773 0.511 11.309 0.000
x2 -1.321 0.479 -2.757 0.006
x3 1.135 0.446 2.545 0.011
x4 0.271 0.466 0.581 0.561

Variances:
Estimate Std.Err z-value P(>|z|)
.y 2075.100 293.463 7.071 0.000

注：fit1 和 fit2 Std.err存在微小差异的原因

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多元因变量回归

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sem_Model2 <- 'y1 ~ x1 + x2 + x3 + x4
y2 ~ x1 + x2 + x3 + x4 '
fit2 <- sem(model = sem_Model2,data = myData)
summary(fit2)

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lavaan 0.6-7 ended normally after 62 iterations

Estimator ML
Optimization method NLMINB
Number of free parameters 11

Number of observations 100

Model Test User Model:

Test statistic 0.000
Degrees of freedom 0

Parameter Estimates:

Standard errors Standard
Information Expected
Information saturated (h1) model Structured

Regressions:
Estimate Std.Err z-value P(>|z|)
y1 ~
x1 4.507 0.426 10.588 0.000
x2 -2.112 0.400 -5.284 0.000
x3 0.888 0.372 2.388 0.017
x4 -0.294 0.388 -0.757 0.449
y2 ~
x1 0.693 0.237 2.924 0.003
x2 -2.721 0.223 -12.230 0.000
x3 0.043 0.207 0.210 0.834
x4 0.724 0.216 3.345 0.001

Covariances:
Estimate Std.Err z-value P(>|z|)
.y1 ~~
.y2 0.906 80.345 0.011 0.991

Variances:
Estimate Std.Err z-value P(>|z|)
.y1 1442.879 204.054 7.071 0.000
.y2 447.393 63.271 7.071 0.000

递归路径分析

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sem_Model3 <- 'x5 ~ x1 + x2 + x3
x6 ~ x4 + x5
x7 ~ x6'
fit3 <- sem(model = sem_Model3,data = myData)
summary(fit3)

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lavaan 0.6-7 ended normally after 47 iterations

Estimator ML
Optimization method NLMINB
Number of free parameters 9

Number of observations 100

Model Test User Model:

Test statistic 7.447
Degrees of freedom 9
P-value (Chi-square) 0.591

Parameter Estimates:

Standard errors Standard
Information Expected
Information saturated (h1) model Structured

Regressions:
Estimate Std.Err z-value P(>|z|)
x5 ~
x1 -0.001 0.002 -0.269 0.788
x2 -0.001 0.002 -0.295 0.768
x3 -0.001 0.002 -0.445 0.657
x6 ~
x4 -0.006 0.033 -0.174 0.862
x5 0.217 1.789 0.121 0.903
x7 ~
x6 -0.014 0.034 -0.399 0.690

Variances:
Estimate Std.Err z-value P(>|z|)
.x5 0.033 0.005 7.071 0.000
.x6 10.714 1.515 7.071 0.000
.x7 1.242 0.176 7.071 0.000

中介分析

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sem_Model4 <- '
y ~ b*y1 + c*y2
y1 ~ a*y2
indirect := a*b
total := c + (a*b)
'
fit4 <- sem(model = sem_Model4,data = myData,se = "bootstrap")
summary(fit4)

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lavaan 0.6-7 ended normally after 18 iterations

Estimator ML
Optimization method NLMINB
Number of free parameters 5

Number of observations 100

Model Test User Model:

Test statistic 0.000
Degrees of freedom 0

Parameter Estimates:

Standard errors Bootstrap
Number of requested bootstrap draws 1000
Number of successful bootstrap draws 1000

Regressions:
Estimate Std.Err z-value P(>|z|)
y ~
y1 (b) 0.602 0.104 5.788 0.000
y2 (c) 0.240 0.167 1.435 0.151
y1 ~
y2 (a) 0.625 0.166 3.759 0.000

Variances:
Estimate Std.Err z-value P(>|z|)
.y 3477.433 629.078 5.528 0.000
.y1 3114.961 406.549 7.662 0.000

Defined Parameters:
Estimate Std.Err z-value P(>|z|)
indirect 0.376 0.111 3.405 0.001
total 0.617 0.171 3.608 0.000

路径图绘制

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pdf("./img/SEM形式.pdf")
p = semPaths(fit1_2)
p1=semPaths(object = fit1_2,whatLabels = "std", edge.label.cex = 1)
p2 = semPaths(fit2)
p3 = semPaths(fit3)
p4 = semPaths(fit4)
dev.off()

png: 2

4. 实例分析1

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读取数据

该示例数据为lavvan包自带

数据集HolzingerSwineford1939，该数据集内嵌在lavaan包中

构建模型

使用CFA

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HSmodel_1 <- 'visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
'
fit5_1 <- cfa(model = HSmodel_1,data = HolzingerSwineford1939)
summary(fit5_1, fit.measures = TRUE,standardized = TRUE)

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lavaan 0.6-7 ended normally after 35 iterations

Estimator ML
Optimization method NLMINB
Number of free parameters 21

Number of observations 301

Model Test User Model:

Test statistic 85.306
Degrees of freedom 24
P-value (Chi-square) 0.000

Model Test Baseline Model:

Test statistic 918.852
Degrees of freedom 36
P-value 0.000

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.931
Tucker-Lewis Index (TLI) 0.896

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -3737.745
Loglikelihood unrestricted model (H1) -3695.092

Akaike (AIC) 7517.490
Bayesian (BIC) 7595.339
Sample-size adjusted Bayesian (BIC) 7528.739

Root Mean Square Error of Approximation:

RMSEA 0.092
90 Percent confidence interval - lower 0.071
90 Percent confidence interval - upper 0.114
P-value RMSEA <= 0.05 0.001

Standardized Root Mean Square Residual:

SRMR 0.065

Parameter Estimates:

Standard errors Standard
Information Expected
Information saturated (h1) model Structured

Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual =~
x1 1.000 0.900 0.772
x2 0.554 0.100 5.554 0.000 0.498 0.424
x3 0.729 0.109 6.685 0.000 0.656 0.581
textual =~
x4 1.000 0.990 0.852
x5 1.113 0.065 17.014 0.000 1.102 0.855
x6 0.926 0.055 16.703 0.000 0.917 0.838
speed =~
x7 1.000 0.619 0.570
x8 1.180 0.165 7.152 0.000 0.731 0.723
x9 1.082 0.151 7.155 0.000 0.670 0.665

Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual ~~
textual 0.408 0.074 5.552 0.000 0.459 0.459
speed 0.262 0.056 4.660 0.000 0.471 0.471
textual ~~
speed 0.173 0.049 3.518 0.000 0.283 0.283

Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 0.549 0.114 4.833 0.000 0.549 0.404
.x2 1.134 0.102 11.146 0.000 1.134 0.821
.x3 0.844 0.091 9.317 0.000 0.844 0.662
.x4 0.371 0.048 7.779 0.000 0.371 0.275
.x5 0.446 0.058 7.642 0.000 0.446 0.269
.x6 0.356 0.043 8.277 0.000 0.356 0.298
.x7 0.799 0.081 9.823 0.000 0.799 0.676
.x8 0.488 0.074 6.573 0.000 0.488 0.477
.x9 0.566 0.071 8.003 0.000 0.566 0.558
visual 0.809 0.145 5.564 0.000 1.000 1.000
textual 0.979 0.112 8.737 0.000 1.000 1.000
speed 0.384 0.086 4.451 0.000 1.000 1.000

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#当均值结构参数设置为真时meanstructure=TRUE，均值结构被添加到模型中
fit5_11 <- cfa(model = HSmodel_1, data=HolzingerSwineford1939, meanstructure=TRUE)
summary(fit5_11)

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lavaan 0.6-5 ended normally after 35 iterations

Estimator ML
Optimization method NLMINB
Number of free parameters 30

Number of observations 301

Model Test User Model:

Test statistic 85.306
Degrees of freedom 24
P-value (Chi-square) 0.000

Parameter Estimates:

Information Expected
Information saturated (h1) model Structured
Standard errors Standard

Latent Variables:
Estimate Std.Err z-value P(>|z|)
visual =~
x1 1.000
x2 0.554 0.100 5.554 0.000
x3 0.729 0.109 6.685 0.000
textual =~
x4 1.000
x5 1.113 0.065 17.014 0.000
x6 0.926 0.055 16.703 0.000
speed =~
x7 1.000
x8 1.180 0.165 7.152 0.000
x9 1.082 0.151 7.155 0.000

Covariances:
Estimate Std.Err z-value P(>|z|)
visual ~~
textual 0.408 0.074 5.552 0.000
speed 0.262 0.056 4.660 0.000
textual ~~
speed 0.173 0.049 3.518 0.000

Intercepts:
Estimate Std.Err z-value P(>|z|)
.x1 4.936 0.067 73.473 0.000
.x2 6.088 0.068 89.855 0.000
.x3 2.250 0.065 34.579 0.000
.x4 3.061 0.067 45.694 0.000
.x5 4.341 0.074 58.452 0.000
.x6 2.186 0.063 34.667 0.000
.x7 4.186 0.063 66.766 0.000
.x8 5.527 0.058 94.854 0.000
.x9 5.374 0.058 92.546 0.000
visual 0.000
textual 0.000
speed 0.000

Variances:
Estimate Std.Err z-value P(>|z|)
.x1 0.549 0.114 4.833 0.000
.x2 1.134 0.102 11.146 0.000
.x3 0.844 0.091 9.317 0.000
.x4 0.371 0.048 7.779 0.000
.x5 0.446 0.058 7.642 0.000
.x6 0.356 0.043 8.277 0.000
.x7 0.799 0.081 9.823 0.000
.x8 0.488 0.074 6.573 0.000
.x9 0.566 0.071 8.003 0.000
visual 0.809 0.145 5.564 0.000
textual 0.979 0.112 8.737 0.000
speed 0.384 0.086 4.451 0.000

使用SEM

1 2	fit5_2 <- cfa(model = HSmodel_1,data = HolzingerSwineford1939) summary(fit5_2, fit.measures = TRUE,standardized = TRUE)

使用lavvan

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HSmodel_3 <- '
# latent variables
visual =~ 1*x1 + x2 + x3
textual =~ 1*x4 + x5 + x6
speed =~ 1*x7 + x8 + x9
# factor (co)variances
visual ~~ visual; visual ~~ textual; visual ~~ speed
textual ~~ textual; textual ~~ speed
speed ~~ speed
# residual variances
x1 ~~ x1; x2 ~~ x2; x3 ~~ x3
x4 ~~ x4; x5 ~~ x5; x6 ~~ x6
x7 ~~ x7; x8 ~~ x8; x9 ~~ x9
'

fit5_3 <- lavaan(model = HSmodel_3, data = HolzingerSwineford1939)
summary(fit5_3, fit.measures=TRUE,standardized=TRUE)

lavaan 0.6-7 ended normally after 35 iterations

Estimator ML
Optimization method NLMINB
Number of free parameters 21

Number of observations 301

Model Test User Model:

Test statistic 85.306
Degrees of freedom 24
P-value (Chi-square) 0.000

Model Test Baseline Model:

Test statistic 918.852
Degrees of freedom 36
P-value 0.000

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.931
Tucker-Lewis Index (TLI) 0.896

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -3737.745
Loglikelihood unrestricted model (H1) -3695.092

Akaike (AIC) 7517.490
Bayesian (BIC) 7595.339
Sample-size adjusted Bayesian (BIC) 7528.739

Root Mean Square Error of Approximation:

RMSEA 0.092
90 Percent confidence interval - lower 0.071
90 Percent confidence interval - upper 0.114
P-value RMSEA <= 0.05 0.001

Standardized Root Mean Square Residual:

SRMR 0.065

Parameter Estimates:

Standard errors Standard
Information Expected
Information saturated (h1) model Structured

Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual =~
x1 1.000 0.900 0.772
x2 0.554 0.100 5.554 0.000 0.498 0.424
x3 0.729 0.109 6.685 0.000 0.656 0.581
textual =~
x4 1.000 0.990 0.852
x5 1.113 0.065 17.014 0.000 1.102 0.855
x6 0.926 0.055 16.703 0.000 0.917 0.838
speed =~
x7 1.000 0.619 0.570
x8 1.180 0.165 7.152 0.000 0.731 0.723
x9 1.082 0.151 7.155 0.000 0.670 0.665

Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual ~~
textual 0.408 0.074 5.552 0.000 0.459 0.459
speed 0.262 0.056 4.660 0.000 0.471 0.471
textual ~~
speed 0.173 0.049 3.518 0.000 0.283 0.283

Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual 0.809 0.145 5.564 0.000 1.000 1.000
textual 0.979 0.112 8.737 0.000 1.000 1.000
speed 0.384 0.086 4.451 0.000 1.000 1.000
.x1 0.549 0.114 4.833 0.000 0.549 0.404
.x2 1.134 0.102 11.146 0.000 1.134 0.821
.x3 0.844 0.091 9.317 0.000 0.844 0.662
.x4 0.371 0.048 7.779 0.000 0.371 0.275
.x5 0.446 0.058 7.642 0.000 0.446 0.269
.x6 0.356 0.043 8.277 0.000 0.356 0.298
.x7 0.799 0.081 9.823 0.000 0.799 0.676
.x8 0.488 0.074 6.573 0.000 0.488 0.477
.x9 0.566 0.071 8.003 0.000 0.566 0.558

多组别分析

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# model 1: configural invariance
fit5_41 <- cfa(HSmodel_1, data=HolzingerSwineford1939, group="school")
# model 2: weak invariance
fit5_42 <- cfa(HSmodel_1, data=HolzingerSwineford1939, group="school",group.equal="loadings")
# model 3: strong invariance
fit5_43 <- cfa(HSmodel_1, data=HolzingerSwineford1939, group="school",group.equal=c("loadings", "intercepts"))
# model 4: equal loadings + intercepts + means
fit5_44 <- cfa(HSmodel_1, data=HolzingerSwineford1939, group="school",group.equal=c("loadings", "intercepts", "means"))

两模型比较（anova）

1	anova(fit5_41, fit5_42)

A anova: 2 × 7
	Df	AIC	BIC	Chisq	Chisq diff	Df diff	Pr(>Chisq)

fit5_41	48	7484.395	7706.822	115.8513	NA	NA	NA
fit5_42	54	7480.587	7680.771	124.0435	8.1922	6	0.2243577

测量不变性检验（semTools -> measurementInvariance）

两两比较

1	measurementInvariance(HSmodel_1, data=HolzingerSwineford1939,group="school", strict=FALSE)

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Error in library(semTools): there is no package called 'semTools'
Traceback:

1. library(semTools)

2. stop(txt, domain = NA)

缺失数据处理 FIML ( full informationmaximum likelihood ) estimation

1）随机缺失（lavvan中可解决）

MCAR (missing completely at random):数据缺失完全随机，估计结果无偏

MAR (missing at random)：缺失数据不依赖于缺失数据本身，可能与未缺失数据有关

2）非随机缺失

NMAR(not missing at random): 一般来说，几乎所有的标准统计方法都不再有效。我们只能试着了解其缺失机制，并在建模数据时考虑到这一点。

1	fit5_5 <- cfa(HSmodel_1, data = HSmissing,missing = "ml") # or missing = "fiml"

绘制路径图

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dev.new()
pdf("./img/实例分析1.pdf")
#初始图
fitname = fit5_3
p = semPaths(fitname)
#含系数的图
p1=semPaths(object = fitname,whatLabels = "std", edge.label.cex = 1)
#不同形状的图
p2=semPaths(object = fitname,layout = "circle")
p3=semPaths(object = fitname,layout = "tree2")
p4=semPaths(object = fitname,layout = "circle2")
p5=semPaths(object = fitname,layout = "spring")
#旋转图
p6 = semPaths(fitname,rotation=2)
#线条颜色设置
p7 = semPaths(fitname,rotation=2,edge.color = "blue")
#变量颜色设置
p8 = semPaths(fitname,rotation=2,edge.color = "blue",color = "lightblue",whatLabels = "std", edge.label.cex = 1)
#分组

p9 = semPaths(fit5_41,rotation=2,edge.color = "blue",color = "lightblue",whatLabels = "std", edge.label.cex = 1 )

p10 = semPaths(fit5_41,rotation=2,whatLabels = "std", edge.label.cex = 1,groups="latents" )

dev.off()

png: 2

5. 实例分析2(带约束的SEM)

在这里插入图片描述

模型构建

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PDmodel <- '
# latent variable definitions
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + a*y2 + b*y3 + c*y4
dem65 =~ y5 + a*y6 + b*y7 + c*y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
# residual covariances
y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8
'

结果输出

1 2	fit6 <- sem(PDmodel, data=PoliticalDemocracy) summary(fit6, standardized=TRUE)

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lavaan 0.6-7 ended normally after 66 iterations

Estimator ML
Optimization method NLMINB
Number of free parameters 31
Number of equality constraints 3

Number of observations 75

Model Test User Model:

Test statistic 40.179
Degrees of freedom 38
P-value (Chi-square) 0.374

Parameter Estimates:

Standard errors Standard
Information Expected
Information saturated (h1) model Structured

Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ind60 =~
x1 1.000 0.670 0.920
x2 2.180 0.138 15.751 0.000 1.460 0.973
x3 1.818 0.152 11.971 0.000 1.218 0.872
dem60 =~
y1 1.000 2.201 0.850
y2 (a) 1.191 0.139 8.551 0.000 2.621 0.690
y3 (b) 1.175 0.120 9.755 0.000 2.586 0.758
y4 (c) 1.251 0.117 10.712 0.000 2.754 0.838
dem65 =~
y5 1.000 2.154 0.817
y6 (a) 1.191 0.139 8.551 0.000 2.565 0.755
y7 (b) 1.175 0.120 9.755 0.000 2.530 0.802
y8 (c) 1.251 0.117 10.712 0.000 2.694 0.829

Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
dem60 ~
ind60 1.471 0.392 3.750 0.000 0.448 0.448
dem65 ~
ind60 0.600 0.226 2.661 0.008 0.187 0.187
dem60 0.865 0.075 11.554 0.000 0.884 0.884

Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y1 ~~
.y5 0.583 0.356 1.637 0.102 0.583 0.281
.y2 ~~
.y4 1.440 0.689 2.092 0.036 1.440 0.291
.y6 2.183 0.737 2.960 0.003 2.183 0.356
.y3 ~~
.y7 0.712 0.611 1.165 0.244 0.712 0.169
.y4 ~~
.y8 0.363 0.444 0.817 0.414 0.363 0.111
.y6 ~~
.y8 1.372 0.577 2.378 0.017 1.372 0.338

Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 0.081 0.019 4.182 0.000 0.081 0.154
.x2 0.120 0.070 1.729 0.084 0.120 0.053
.x3 0.467 0.090 5.177 0.000 0.467 0.239
.y1 1.855 0.433 4.279 0.000 1.855 0.277
.y2 7.581 1.366 5.549 0.000 7.581 0.525
.y3 4.956 0.956 5.182 0.000 4.956 0.426
.y4 3.225 0.723 4.458 0.000 3.225 0.298
.y5 2.313 0.479 4.831 0.000 2.313 0.333
.y6 4.968 0.921 5.393 0.000 4.968 0.430
.y7 3.560 0.710 5.018 0.000 3.560 0.357
.y8 3.308 0.704 4.701 0.000 3.308 0.313
ind60 0.449 0.087 5.175 0.000 1.000 1.000
.dem60 3.875 0.866 4.477 0.000 0.800 0.800
.dem65 0.164 0.227 0.725 0.469 0.035 0.035

绘制路径图

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dev.new()
pdf("./img/实例分析2.pdf")
#初始图
p = semPaths(fit6)
#含系数的图
p1=semPaths(object = fit6,whatLabels = "std", edge.label.cex = 1)
#不同形状的图
p2=semPaths(object = fit6,layout = "circle")
p3=semPaths(object = fit6,layout = "tree2")
p4=semPaths(object = fit6,layout = "circle2")
p5=semPaths(object = fit6,layout = "spring")
#旋转图
p6 = semPaths(fit6,rotation=2)
#线条颜色设置
p7 = semPaths(fit6,rotation=2,edge.color = "blue")
#变量颜色设置
p8 = semPaths(fit6,rotation=2,edge.color = "blue",color = "lightblue",whatLabels = "std", edge.label.cex = 1)
dev.off()

# dev.new()
# pdf("./img/实例分析2.pdf")
# #初始图
# title("Regression of MPG on Weight")
# p = semPaths(fit6,title=TRUE,"图1 实例分析2（初始tree）", title.color = "black")
# #含系数的图
# p1=semPaths(object = fit6,title="图2 实例分析2路径系数", title.color = "black",whatLabels = "std", edge.label.cex = 1)
# #不同形状的图
# p2=semPaths(object = fit6,title="图3 实例分析2（初始circle）", title.color = "black",layout = "circle")
# spring;tree2;circle2
# p3=semPaths(object = fit6,title="图4 实例分析2（初始tree2）", title.color = "black",layout = "tree2")
# p4=semPaths(object = fit6,title="图5 实例分析2（初始circle2）",title.color = "black",layout = "circle2")
# p5=semPaths(object = fit6,title="图6 实例分析2（初始spring）", title.color = "black",layout = "spring")
# #旋转图
# p6 = semPaths(fit6,title="图7 实例分析2（初始tree旋转）", title.color = "black",rotation=2)
# #线条颜色设置
# p7 = semPaths(fit6,title="图8 实例分析2（初始tree旋转蓝线条）", title.color = "black",rotation=2,edge.color = "blue")
# #变量颜色设置
# p8 = semPaths(fit6,title="图9 实例分析2（初始tree旋转蓝）", title.color = "black",rotation=2,edge.color = "blue",color = "blue")
# dev.off()

png: 2

6. 连续非正态数据和替代估计量

连续非正态数据：左偏、右偏、尖峰、厚尾等

常见三种处理方法：

ADF(asymptotically distribution-free) estimation

2)ML(maximum likelihood)

3)bootstrapping

方法1：ADF

ADF估计量(Browne, 1984)无正态性假设，称为加权最小二乘(WLS)估计

研究表明，只有样本量很大(例如，N > 5000)时效果较好，否则ADF方法会失败

1	fit5_6 <- cfa(HSmodel_1, data = HolzingerSwineford1939,estimator = "WLS")

方法2：ML

1 2	# robust standard errors fit5_71 <- cfa(HSmodel_1, data = HolzingerSwineford1939,,se = "robust")

1 2	#Satorra-Bentler scaled test statistic fit5_72 <- cfa(HSmodel_1, data = HolzingerSwineford1939,test = "Satorra-Bentler")

1 2	# Robust standard errors + scaled test statistic fit5_73 <- cfa(HSmodel_1, data = HolzingerSwineford1939,se = "robust", test = "Satorra-Bentler")

1 2	# estimator MLM = robust standard errors + scaled test statistic fit5_74 <- cfa(HSmodel_1, data = HolzingerSwineford1939,estimator = "MLM")

1 2	# alternative: estimator MLR (同时含缺失数据) fit5_75 <- cfa(HSmodel_1, data = HolzingerSwineford1939,estimator = "MLR", missing = "ml")

方法3：bootstrapping

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# bootstrapping standard errors:(可输出置信区间)
fit5_81 <- cfa(HSmodel_1, data = HolzingerSwineford1939,se = "bootstrap", verbose = TRUE, bootstrap = 1000)
# bootstrapping the test statistic
fit5_82 <- cfa(HSmodel_1, data = HolzingerSwineford1939,test = "bootstrap", verbose = TRUE, bootstrap = 1000)

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Quasi-Newton steps using NLMINB:
Objective function = 2.0640106626333683
Objective function = 0.5481724334022804
Objective function = 0.4744000434739597
Objective function = 0.3116651572650557
Objective function = 0.2935347771542274
Objective function = 0.2091927643393836
Objective function = 0.1986590305865628
Objective function = 0.1549912702721032
Objective function = 0.1519382593582579
Objective function = 0.1472224332311631
。。。。。。。部分结果略。。。。。。
... bootstrap draw number: 999 OK -- niter = 26 fx = 0.158705135
... bootstrap draw number: 1000 OK -- niter = 26 fx = 0.244148094
Number of successful bootstrap draws: 1000
done.
Computing TEST for test(s) = standard ... done.
Fitting baseline model ... done.
Quasi-Newton steps using NLMINB:
Objective function = 2.0640106626333683
Objective function = 0.5481724334022804
Objective function = 0.4744000434739597
Objective function = 0.3116651572650557
Objective function = 0.2935347771542274

。。。。。。。部分结果略。。。。。。
… bootstrap draw number: 999 OK – niter = 25 fx = 0.041584423
… bootstrap draw number: 1000 OK – niter = 27 fx = 0.045263513
Number of successful bootstrap draws: 1000
done.
Fitting baseline model … done.

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# 使用bootstrapLavaan()计算Bolen-Stine p值(可配置)
fit5_83 <- cfa(HSmodel_1, data=HolzingerSwineford1939, se="none")

T.orig <- fitMeasures(fit5_83, "chisq")

T.boot <- bootstrapLavaan(fit5_83,R = 10,type = "bollen.stine",FUN = fitMeasures,fit5_83.measures = "chisq")

pvalue.boot <- length(which(T.boot > T.orig))/length(T.boot)

7. 分类内生变量

二分类数据、多分类数据、定序数据、计数数据、生存数据

常见三种处理方法：

WLSMV , logit/probit

方法1：阈值法连续化

观察到的变量y通常可以看作是对潜在的连续响应y*的部分观察。

例如:K =4 的有序响应变量类别:
在这里插入图片描述

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# generate ‘ordered’ data with 4 categories
y_ord4 <- sample(1:4, size = 100, replace = TRUE)
prop <- table(Y)/sum(table(Y))
cprop <- c(0, cumsum(prop))
th <- qnorm(cprop)

方法2 ：probit

存在外生协变量时，可直接利用probit回归

– tetrachoric (binary – binary)

– polychoric (ordered – ordered)

– polyserial (ordered – numeric)

– biserial (binary – numeric)

– pearson (numeric – numeric)

ordered=c(“item1”,“item2”,“item3”,“item4”)可将多个变量有序化

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library(MASS)
X1 <- rnorm(100)
X2 <- rnorm(100)
X3 <- rnorm(100)
fit7_1 <- polr(ordered(y_ord4) ? X1 + X2 + X3, method = "probit")
fit7_1$zeta

示例：实例1数据

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HS9 <- HolzingerSwineford1939[,c("x1","x2","x3","x4","x5","x6","x7","x8","x9")]
HSbinary <- as.data.frame( lapply(HS9, cut, 2, labels=FALSE) )
# binary CFA
fit7_2 <- cfa(HSmodel_1, data=HSbinary, ordered=names(HSbinary))
summary(fit7_2,fit7_2.measures=TRUE)

1	inspect(fit7_2, "sampstat")

8. 提取函数应用示例

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#见实例分析1
HSmodel_1 <- 'visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
'

1	fit8 <- cfa(HSmodel_1, data=HolzingerSwineford1939)

1	fitted(fit8)

$cov =

A lavaan.matrix.symmetric: 9 × 9 of type dbl
	x1	x2	x3	x4	x5	x6	x7	x8	x9
x1	1.3583700	0.4479566	0.5902910	0.4082324	0.4543940	0.3780829	0.2622246	0.3094121	0.2836038
x2	0.4479566	1.3817831	0.3267262	0.2259568	0.2515072	0.2092690	0.1451414	0.1712597	0.1569748
x3	0.5902910	0.3267262	1.2748647	0.2977526	0.3314214	0.2757624	0.1912588	0.2256760	0.2068522
x4	0.4082324	0.2259568	0.2977526	1.3506644	1.0902489	0.9071522	0.1734947	0.2047152	0.1876397
x5	0.4543940	0.2515072	0.3314214	1.0902489	1.6597856	1.0097299	0.1931129	0.2278637	0.2088574
x6	0.3780829	0.2092690	0.2757624	0.9071522	1.0097299	1.1963583	0.1606814	0.1895962	0.1737818
x7	0.2622246	0.1451414	0.1912588	0.1734947	0.1931129	0.1606814	1.1831393	0.4528034	0.4150347
x8	0.3094121	0.1712597	0.2256760	0.2047152	0.2278637	0.1895962	0.4528034	1.0219828	0.4897205
x9	0.2836038	0.1569748	0.2068522	0.1876397	0.2088574	0.1737818	0.4150347	0.4897205	1.0150038

1	predict(fit8)

A lavaan.matrix: 301 × 3 of type dbl
visual	textual	speed
-0.81767524	-0.13754501	0.06150726
0.04951940	-1.01272402	0.62549360
-0.76139670	-1.87228634	-0.84057276
0.41934153	0.01848569	-0.27133710
-0.41590481	-0.12225009	0.19432951
0.02325632	-1.32981727	0.70885348
-0.98496789	0.65761381	0.04370647
0.10684376	-0.10512788	-0.53230194
-0.25397131	0.40433106	0.20036715
-1.05421886	0.09291512	-0.56666789
-0.75848238	-0.76939476	-0.32272938
0.39808636	0.09621166	-0.36351841
0.51898256	-0.14038719	0.28709094
0.24108494	0.21574804	-0.24259754
0.70257424	1.15797443	-0.12973764
-0.42473596	-0.59549971	-0.55369318
-0.58761600	-0.69464666	0.12080778
-0.05083838	-0.95018913	-0.10375995
0.66490790	1.09597201	-0.04174159
0.97772373	0.18795244	-0.12304567
0.23952816	-1.35930395	-0.43925580
1.33320492	-0.52348581	0.47433613
-0.01872902	0.72510961	-0.39098728
-0.65236812	-0.85126858	0.35389317
-0.14193523	-0.64671143	-0.44254826
0.07459743	-0.84369449	0.17047103
0.35906264	-1.08215625	-0.26763982
0.06073595	-1.07208831	-0.37789768
0.36284640	-0.68722561	0.87878736
-0.53281609	-0.54291209	-0.16260680
...	...	...
0.36579463	0.286998384	0.16020380
-0.11301304	-0.008594389	0.78275251
-0.31322664	-0.117325314	0.02863657
0.43165862	-0.552461192	0.39482293
-1.05019439	-0.817906236	-0.76617073
-0.17358766	0.021497247	-0.40875089
-0.05252645	0.367863096	-0.17593087
0.15839234	-0.792699519	0.50487360
0.57832663	-0.121716586	0.30412862
-0.88456464	-0.452929413	0.11865986
0.30021737	1.335667006	-0.78516652
-0.61851705	-0.260155389	-0.71446297
0.72163334	0.713018089	-0.32928632
-0.14855811	-0.477111209	0.51598547
0.14577715	-0.219169373	-0.08770218
0.56806351	1.606779375	0.09576261
-0.46039523	-0.501810492	0.41742089
-0.49595506	0.380804720	0.41931919
0.39787129	-0.001286655	-0.20616710
-1.00453500	-0.370879351	0.37667244
-0.49694338	-1.079965387	-0.12580818
0.14006996	0.014458282	0.12929032
0.24014891	0.086748659	0.01910399
0.18492002	-0.477628434	-0.08199923
0.62226627	0.181525443	-0.34620461
-0.49495815	-0.507343016	0.05023989
-0.93999794	-0.698817917	0.21812239
0.03677903	1.169004482	0.56918416
-0.47087734	0.138702247	0.04466651
0.14776003	0.848046807	0.33771119

1	inspect(fit8) # matrix representation

$lambda

A lavaan.matrix: 9 × 3 of type dbl
	visual	textual	speed
x1	0	0	0
x2	1	0	0
x3	2	0	0
x4	0	0	0
x5	0	3	0
x6	0	4	0
x7	0	0	0
x8	0	0	5
x9	0	0	6

$theta

A lavaan.matrix.symmetric: 9 × 9 of type dbl
	x1	x2	x3	x4	x5	x6	x7	x8	x9
x1	7	0	0	0	0	0	0	0	0
x2	0	8	0	0	0	0	0	0	0
x3	0	0	9	0	0	0	0	0	0
x4	0	0	0	10	0	0	0	0	0
x5	0	0	0	0	11	0	0	0	0
x6	0	0	0	0	0	12	0	0	0
x7	0	0	0	0	0	0	13	0	0
x8	0	0	0	0	0	0	0	14	0
x9	0	0	0	0	0	0	0	0	15

$psi

A lavaan.matrix.symmetric: 3 × 3 of type dbl
	visual	textual	speed
visual	16	19	20
textual	19	17	21
speed	20	21	18

1	inspect(fit8, "sampstat")

$cov =

A lavaan.matrix.symmetric: 9 × 9 of type dbl
	x1	x2	x3	x4	x5	x6	x7	x8	x9
x1	1.35836985	0.40737133	0.57989932	0.5048350	0.4406155	0.4548081	0.08476543	0.2638377	0.4583385
x2	0.40737133	1.38178387	0.45106394	0.2089234	0.2110911	0.2475446	-0.09675102	0.1096594	0.2440095
x3	0.57989932	0.45106394	1.27486486	0.2081696	0.1122963	0.2441090	0.08834184	0.2123226	0.3738526
x4	0.50483500	0.20892337	0.20816961	1.3506645	1.0977528	0.8955157	0.21974259	0.1255933	0.2433627
x5	0.44061554	0.21109108	0.11229629	1.0977528	1.6597858	1.0145240	0.14299955	0.1806052	0.2952413
x6	0.45480813	0.24754457	0.24410898	0.8955157	1.0145240	1.1963584	0.14407839	0.1654310	0.2359969
x7	0.08476543	-0.09675102	0.08834184	0.2197426	0.1429995	0.1440784	1.18313946	0.5352452	0.3732972
x8	0.26383768	0.10965939	0.21232264	0.1255933	0.1806052	0.1654310	0.53524522	1.0219828	0.4573166
x9	0.45833855	0.24400945	0.37385257	0.2433627	0.2952413	0.2359969	0.37329722	0.4573166	1.0150039

1	fitMeasures(fit8)

npar

fmin

0.141703524534838

chisq

85.3055217699727

pvalue

8.50255321704907e-09

baseline.chisq

918.851589292384

baseline.df

baseline.pvalue

cfi

0.930559651799336

tli

0.895839477699004

nnfi

0.895839477699004

rfi

0.86074107707263

nfi

0.90716071804842

pnfi

0.60477381203228

ifi

0.931490849987258

rni

0.930559651799336

logl

-3737.7449266262

unrestricted.logl

-3695.09216574121

aic

7517.48985325239

bic

7595.33916881212

ntotal

301

bic2

7528.73911173078

rmsea

0.0921214845101686

rmsea.ci.lower

0.0714184904399382

rmsea.ci.upper

0.113678016811963

rmsea.pvalue

0.000661236778051855

rmr

0.0821843333342268

rmr_nomean

0.0821843333342268

srmr

0.0652050571843865

srmr_bentler

0.0652050571843865

srmr_bentler_nomean

0.0652050571843865

crmr

0.0729014727869723

crmr_nomean

0.0729014727869723

srmr_mplus

0.0652050595246683

srmr_mplus_nomean

0.0652050595246683

cn_05

129.490200301456

cn_01

152.654026533352

gfi

0.943332061258476

agfi

0.893747614859642

pgfi

0.503110432671187

mfi

0.903177285931363

ecvi

0.422941932790607

1	parameterTable(fit8)

A lavaan.data.frame: 24 × 15
id	lhs	op	rhs	user	block	group	free	ustart	exo	plabel	start	est	se

1	visual	=~	x1	1	1	1	0	1	0	.p1.	1.0000000	1.0000000	0.00000000
2	visual	=~	x2	1	1	1	1	NA	0	.p2.	0.7778315	0.5535003	0.09966512
3	visual	=~	x3	1	1	1	2	NA	0	.p3.	1.1072550	0.7293702	0.10910970
4	textual	=~	x4	1	1	1	0	1	0	.p4.	1.0000000	1.0000000	0.00000000
5	textual	=~	x5	1	1	1	3	NA	0	.p5.	1.1328936	1.1130766	0.06542011
6	textual	=~	x6	1	1	1	4	NA	0	.p6.	0.9241826	0.9261462	0.05544886
7	speed	=~	x7	1	1	1	0	1	0	.p7.	1.0000000	1.0000000	0.00000000
8	speed	=~	x8	1	1	1	5	NA	0	.p8.	1.2250736	1.1799508	0.16498657
9	speed	=~	x9	1	1	1	6	NA	0	.p9.	0.8544057	1.0815302	0.15116744
10	x1	~~	x1	0	1	1	7	NA	0	.p10.	0.6791849	0.5490540	0.11360092
11	x2	~~	x2	0	1	1	8	NA	0	.p11.	0.6908919	1.1338390	0.10172337
12	x3	~~	x3	0	1	1	9	NA	0	.p12.	0.6374324	0.8443240	0.09062318
13	x4	~~	x4	0	1	1	10	NA	0	.p13.	0.6753323	0.3711730	0.04771779
14	x5	~~	x5	0	1	1	11	NA	0	.p14.	0.8298929	0.4462551	0.05839278
15	x6	~~	x6	0	1	1	12	NA	0	.p15.	0.5981792	0.3562027	0.04303497
16	x7	~~	x7	0	1	1	13	NA	0	.p16.	0.5915697	0.7993916	0.08138156
17	x8	~~	x8	0	1	1	14	NA	0	.p17.	0.5109914	0.4876971	0.07419409
18	x9	~~	x9	0	1	1	15	NA	0	.p18.	0.5075019	0.5661313	0.07073694
19	visual	~~	visual	0	1	1	16	NA	0	.p19.	0.0500000	0.8093160	0.14546241
20	textual	~~	textual	0	1	1	17	NA	0	.p20.	0.0500000	0.9794914	0.11210585
21	speed	~~	speed	0	1	1	18	NA	0	.p21.	0.0500000	0.3837476	0.08620919
22	visual	~~	textual	0	1	1	19	NA	0	.p22.	0.0000000	0.4082324	0.07352388
23	visual	~~	speed	0	1	1	20	NA	0	.p23.	0.0000000	0.2622246	0.05627640
24	textual	~~	speed	0	1	1	21	NA	0	.p24.	0.0000000	0.1734947	0.04931466

1	parameterEstimates(fit8)

A lavaan.data.frame: 24 × 9
lhs	op	rhs	est	se	z	pvalue	ci.lower	ci.upper

visual	=~	x1	1.0000000	0.00000000	NA	NA	1.00000000	1.0000000
visual	=~	x2	0.5535003	0.09966512	5.553601	2.798440e-08	0.35816025	0.7488403
visual	=~	x3	0.7293702	0.10910970	6.684742	2.313327e-11	0.51551912	0.9432213
textual	=~	x4	1.0000000	0.00000000	NA	NA	1.00000000	1.0000000
textual	=~	x5	1.1130766	0.06542011	17.014288	0.000000e+00	0.98485552	1.2412976
textual	=~	x6	0.9261462	0.05544886	16.702711	0.000000e+00	0.81746848	1.0348240
speed	=~	x7	1.0000000	0.00000000	NA	NA	1.00000000	1.0000000
speed	=~	x8	1.1799508	0.16498657	7.151799	8.564260e-13	0.85658310	1.5033186
speed	=~	x9	1.0815302	0.15116744	7.154518	8.397727e-13	0.78524742	1.3778129
x1	~~	x1	0.5490540	0.11360092	4.833182	1.343676e-06	0.32640025	0.7717077
x2	~~	x2	1.1338390	0.10172337	11.146298	0.000000e+00	0.93446487	1.3332132
x3	~~	x3	0.8443240	0.09062318	9.316866	0.000000e+00	0.66670587	1.0219422
x4	~~	x4	0.3711730	0.04771779	7.778503	7.327472e-15	0.27764784	0.4646981
x5	~~	x5	0.4462551	0.05839278	7.642299	2.131628e-14	0.33180733	0.5607028
x6	~~	x6	0.3562027	0.04303497	8.277052	2.220446e-16	0.27185568	0.4405497
x7	~~	x7	0.7993916	0.08138156	9.822761	0.000000e+00	0.63988671	0.9588966
x8	~~	x8	0.4876971	0.07419409	6.573260	4.922529e-11	0.34227934	0.6331148
x9	~~	x9	0.5661313	0.07073694	8.003333	1.110223e-15	0.42748944	0.7047731
visual	~~	visual	0.8093160	0.14546241	5.563747	2.640432e-08	0.52421490	1.0944171
textual	~~	textual	0.9794914	0.11210585	8.737201	0.000000e+00	0.75976795	1.1992148
speed	~~	speed	0.3837476	0.08620919	4.451354	8.533051e-06	0.21478073	0.5527146
visual	~~	textual	0.4082324	0.07352388	5.552379	2.818082e-08	0.26412828	0.5523366
visual	~~	speed	0.2622246	0.05627640	4.659584	3.168493e-06	0.15192489	0.3725243
textual	~~	speed	0.1734947	0.04931466	3.518116	4.346227e-04	0.07683973	0.2701496

1	varTable(fit8)

A lavaan.data.frame: 9 × 10
name	idx	nobs	type	exo	user	mean	var	nlev

x1	7	301	numeric	0	0	4.935770	1.362898	0
x2	8	301	numeric	0	0	6.088040	1.386390	0
x3	9	301	numeric	0	0	2.250415	1.279114	0
x4	10	301	numeric	0	0	3.060908	1.355167	0
x5	11	301	numeric	0	0	4.340532	1.665318	0
x6	12	301	numeric	0	0	2.185572	1.200346	0
x7	13	301	numeric	0	0	4.185902	1.187083	0
x8	14	301	numeric	0	0	5.527076	1.025389	0
x9	15	301	numeric	0	0	5.374123	1.018387	0

1	subset(modindices(fit8), mi > 5)

A lavaan.data.frame: 15 × 8
	lhs	op	rhs	mi	epc	sepc.lv	sepc.all	sepc.nox

26	visual	=~	x5	7.440646	-0.20989801	-0.18882843	-0.1465688	-0.1465688
28	visual	=~	x7	18.630638	-0.42186239	-0.37951580	-0.3489088	-0.3489088
30	visual	=~	x9	36.411031	0.57702154	0.51910006	0.5152491	0.5152491
31	textual	=~	x1	8.902732	0.35033114	0.34672012	0.2974884	0.2974884
33	textual	=~	x3	9.150895	-0.27163761	-0.26883773	-0.2380993	-0.2380993
48	x1	~~	x7	5.419590	-0.12911266	-0.12911266	-0.1948864	-0.1948864
50	x1	~~	x9	7.334930	0.13789383	0.13789383	0.2473311	0.2473311
51	x2	~~	x3	8.531827	0.21823928	0.21823928	0.2230502	0.2230502
55	x2	~~	x7	8.918022	-0.18272538	-0.18272538	-0.1919302	-0.1919302
59	x3	~~	x5	7.858085	-0.13009466	-0.13009466	-0.2119402	-0.2119402
65	x4	~~	x6	6.220497	-0.23480293	-0.23480293	-0.6457535	-0.6457535
66	x4	~~	x7	5.919707	0.09818085	0.09818085	0.1802432	0.1802432
76	x7	~~	x8	34.145089	0.53644397	0.53644397	0.8591510	0.8591510
77	x7	~~	x9	5.182955	-0.18670689	-0.18670689	-0.2775377	-0.2775377
78	x8	~~	x9	14.946392	-0.42309592	-0.42309592	-0.8052026	-0.8052026

9. 加载SEM绘图包（semPlot）

参考资料：

Structural Equation Modeling with lavaan in R
Sacha Epskamp and with contributions from Simon Stuber (2017). semPlot: Path Diagrams and Visual Analysis of Various SEM Packages’
Output. R package version 1.1. https://CRAN.R-project.org/package=semPlot

1 能画出结构方程模型图的软件有很多，比如Amos和SmartPLS，这两个软件在可视化方面做的非常好，Mplus和前两个软件有所不同，它是通过语法输入，从diagrammer生成图形，而Amos和SmartPLS是用户直接绘制图形。

2 R语言也可以绘制结构方程模型图，其优势在于用户可以对SEM图中的变量、线条、形状和颜色进行DIY。本文使用semPlot包中的semPaths函数进行模型图的绘制。

3 使用参数layout来改变图形样式，其可选值包括5种：tree;circle;spring;tree2;circle2

4 大多数人在做CFA的时候会把因子画在左侧，指标画在右侧，这样的图比较适合放在论文中。其实只需要将之前图片样式为tree状的图旋转90°即可。旋转可选的值有：1，2，3，4，分别是默认、逆时针旋转90°、180°以及270°。rotation = 2

5 给线条上色使用参数edge.color，如我们想要深绿色的图，在该参数后写入darkgreen即可。edge.color = “darkgreen”

6 还可以对潜变量或指标配色，直接用color，而非edge.color。 color = “lightblue”

7 如果出现负载荷，图中带有负载荷的线条会变成红色。我们也可以使用posCol，negCol自定义正负载荷的配色

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semPaths(object, what = "paths", whatLabels, style, layout = "tree",
intercepts = TRUE, residuals = TRUE, thresholds = TRUE, intStyle = "multi",
rotation = 1, curve, curvature = 1, nCharNodes = 3, nCharEdges = 3, sizeMan = 5,
sizeLat = 8, sizeInt = 2, sizeMan2, sizeLat2, sizeInt2, shapeMan, shapeLat,
shapeInt = "triangle", ask, mar, title, title.color = "black", title.adj = 0.1,
title.line = -1, title.cex = 0.8, include, combineGroups = FALSE, manifests,
latents, groups, color, residScale, gui = FALSE, allVars = FALSE, edge.color,
reorder = TRUE, structural = FALSE, ThreshAtSide = FALSE, thresholdColor,
thresholdSize = 0.5, fixedStyle = 2, freeStyle = 1,
as.expression = character(0), optimizeLatRes = FALSE, inheritColor = TRUE,
levels, nodeLabels, edgeLabels, pastel = FALSE, rainbowStart = 0, intAtSide,
springLevels = FALSE, nDigits = 2, exoVar, exoCov = TRUE, centerLevels = TRUE,
panelGroups = FALSE, layoutSplit = FALSE, measurementLayout = "tree", subScale,
subScale2, subRes = 4, subLinks, modelOpts = list(mplusStd = "std"),
curveAdjacent = '<->', edge.label.cex = 0.6, cardinal = "none",
equalizeManifests = FALSE, covAtResiduals = TRUE, bifactor, optimPoints = 1:8 * (pi/4),
...)

	x1	x2	x3	x4	x5	x6	x7	x8	x9
x1	7	0	0	0	0	0	0	0	0
x2	0	8	0	0	0	0	0	0	0
x3	0	0	9	0	0	0	0	0	0
x4	0	0	0	10	0	0	0	0	0
x5	0	0	0	0	11	0	0	0	0
x6	0	0	0	0	0	12	0	0	0
x7	0	0	0	0	0	0	13	0	0
x8	0	0	0	0	0	0	0	14	0
x9	0	0	0	0	0	0	0	0	15

	x1	x2	x3	x4	x5	x6	x7	x8	x9
x1	7	0	0	0	0	0	0	0	0
x2	0	8	0	0	0	0	0	0	0
x3	0	0	9	0	0	0	0	0	0
x4	0	0	0	10	0	0	0	0	0
x5	0	0	0	0	11	0	0	0	0
x6	0	0	0	0	0	12	0	0	0
x7	0	0	0	0	0	0	13	0	0
x8	0	0	0	0	0	0	0	14	0
x9	0	0	0	0	0	0	0	0	15

	x1	x2	x3	x4	x5	x6	x7	x8	x9
x1	7	0	0	0	0	0	0	0	0
x2	0	8	0	0	0	0	0	0	0
x3	0	0	9	0	0	0	0	0	0
x4	0	0	0	10	0	0	0	0	0
x5	0	0	0	0	11	0	0	0	0
x6	0	0	0	0	0	12	0	0	0
x7	0	0	0	0	0	0	13	0	0
x8	0	0	0	0	0	0	0	14	0
x9	0	0	0	0	0	0	0	0	15